IPACS Electronic library

Realization theory methods for the construction of positively-invariant sets

Realization theory for linear input-output ope\-rators and
frequency-domain methods for the solvability of Riccati operator equations are used for the stability and instability investigation of a class of nonlinear Volterra integral equations in some Hilbert space. The key idea is to consider, similar to the Volterra equation, a time-invariant control system generated by an abstract ODE in some weighted Sobolev space, which has the same stability properties as the Volterra equation.